1/5(20x+30)-20=-1/2(10x-6)

Solution for 1/5(20x+30)-20=-1/2(10x-6) equation:

1/5(20x+30)-20=-1/2(10x-6)

We move all terms to the left:

1/5(20x+30)-20-(-1/2(10x-6))=0


Domain of the equation: 5(20x+30)!=0

x∈R



Domain of the equation: 2(10x-6))!=0

x∈R


We calculate fractions


(2x1/(5(20x+30)*2(10x-6)))+(-(-5x2)/(5(20x+30)*2(10x-6)))-20=0


We calculate terms in parentheses: +(2x1/(5(20x+30)*2(10x-6))), so:

2x1/(5(20x+30)*2(10x-6))

We multiply all the terms by the denominator


2x1

We add all the numbers together, and all the variables

2x

Back to the equation:

+(2x)



We calculate terms in parentheses: +(-(-5x2)/(5(20x+30)*2(10x-6))), so:

-(-5x2)/(5(20x+30)*2(10x-6))

We add all the numbers together, and all the variables

-(-5x^2)/(5(20x+30)*2(10x-6))

We multiply all the terms by the denominator


-(-5x^2)

We get rid of parentheses

5x^2

Back to the equation:

+(5x^2)


determiningTheFunctionDomain
5x^2+2x-20=0

a = 5; b = 2; c = -20;
Δ = b2-4ac
Δ = 22-4·5·(-20)
Δ = 404
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{404}=\sqrt{4*101}=\sqrt{4}*\sqrt{101}=2\sqrt{101}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{101}}{2*5}=\frac{-2-2\sqrt{101}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{101}}{2*5}=\frac{-2+2\sqrt{101}}{10}
$